Question: In the figure with circle $Q$, angle $KAT$ measures 42 degrees. What is the measure of minor arc $AK$ in degrees? [asy]
import olympiad; size(150); defaultpen(linewidth(0.8)); dotfactor=4;
draw(unitcircle);
draw(dir(84)--(-1,0)--(1,0));
dot("$A$",(-1,0),W); dot("$K$",dir(84),NNE); dot("$T$",(1,0),E); dot("$Q$",(0,0),S);
[/asy]
Explanation: Since $\angle A$ is inscribed in arc $KT$, the measure of arc $KT$ is $2\angle A = 84^\circ$.  Since arc $AKT$ is a semicircle, arc $KA$ has measure $180 - 84 = \boxed{96}$ degrees.